A new coding system to test independence of time series.

Area of Science:

• Time Series Analysis
• Statistical Inference
• Information Theory

Background:

• Time series analysis is crucial in various scientific fields.
• Distinguishing between independent and identically distributed (i.i.d.) time series is a fundamental challenge.
• Existing statistical tests often rely solely on permutation-based methods, potentially limiting their sensitivity.

Purpose of the Study:

• To introduce a novel codification for time series data.
• To develop an improved statistical test for assessing the independence and identical distribution of time series.
• To compare the efficacy of the new test against existing permutation-based approaches.

Main Methods:

• A new time series codification was developed, integrating permutation patterns with quantitative symbolic information.
• This novel codification was used to construct a new statistical test for the i.i.d. hypothesis.
• The performance of the new test was evaluated and compared against traditional permutation-only tests.

Main Results:

• The newly proposed codification effectively captures both structural (permutation) and quantitative aspects of time series.
• The statistical test derived from this enhanced codification demonstrated superior performance.
• Comparative analysis confirmed that the new test yields better results than tests relying exclusively on permutations.

Conclusions:

• The integration of quantitative information into time series codification offers significant advantages for statistical testing.
• The new test provides a more powerful tool for determining if a time series is independent and identically distributed.
• This advancement has implications for improving the reliability of time series analysis across disciplines.